Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×#364 | C2 | semidirect |
| 3. C5×#4455 | C2 | semidirect |
| 12. #67569 | C5 | direct (N × H) |
| 14. C5×#364 | D3 | semidirect |
| 22. C5×Dic12 | C8 | semidirect |
| 23. C5×D24 | C8 | semidirect |
| 29. C3×#364 | C2×C5 | semidirect |
| 30. #4455 | C2×C5 | semidirect |
| 71. #364 | C5×D3 | semidirect |
| 85. Dic12 | C5×C8 | semidirect |
| 86. D24 | C5×C8 | semidirect |
| 143. C3×C5 | #1336 | semidirect |
| 168. C5 | #67569 | direct (N × H) |
| 175. C3 | C5×#1336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4700 | 2 |
| C3×C5×#364 | 2 |
| C5×#4455 | 2 |
| C5×#1336 | 3 |
| #67569 | 5 |